Which of the following equations has the same solution as the equation above? 18/x-3 = 2

Answer 1

To solve for \( x \) in the equation \( \frac{18}{x} - 3 = 2 \), we will first isolate \( \frac{18}{x} \).

1. Add 3 to both sides of the equation: \[ \frac{18}{x} = 2 + 3 \] \[ \frac{18}{x} = 5 \]

2. Now, multiply both sides by \( x \) (assuming \( x \neq 0 \)): \[ 18 = 5x \]

3. Divide both sides by 5: \[ x = \frac{18}{5} \]

Now that we have the solution \( x = \frac{18}{5} \), we can write an equivalent equation.

To derive equations that are equivalent:

1. We can start from the original equation \( \frac{18}{x} - 3 = 2 \) and transform it to a similar format.

2. Multiply through by \( x \) (as indicated earlier): \[ 18 - 3x = 2x \]

3. Rearranging gives us: \[ 18 = 2x + 3x \] \[ 18 = 5x \]

This final expression \( 5x = 18 \) is equivalent to the original equation.

So an equation with the same solution as \( \frac{18}{x} - 3 = 2 \) would be: \[ 5x = 18 \]

If there are any other options specified, please provide them, and I can confirm which one(s) also has the same solution.